Question

Средняя линия трапеции 7 см, а одно из ее оснований больше другого на 4 см. найдите основания трапеции.

Answer 1

Дана трапеция ABCD

MK - средняя линия - 7 см

ВС и AD - основания

AD = BC+4

 

Найти

AD и BC

 

Решение.

Средня линия трапеции равна их полусумме.

ME=1/2*(BC+AD)

7=1/2*(BC+(BC+4))

7=1/2*(2BC+4)

7=BC+2

BC=5 см

 

AD=BC+4=5+4=9 см

 

Ответ BC = 5 см , AD = 9 см

Answer 2

одно основание х, второе х+4. Средняя линия равна 1/2 суммы оснований

1/2 (х+х+4)=7

2х+4=14

х=(14-4):2

х=5, второе основание 9.

Answer 3

Finding the Bases of a Trapezoid

To find the bases of a trapezoid when the midline and the difference between the bases are given, we can use the following formula:

Midline (m) = (a + b) / 2 Difference between bases (d) = |a - b|

Where: - m = midline - a = one base - b = the other base - d = difference between bases

Given: - Midline (m) = 7 cm - Difference between bases (d) = 4 cm

We can use the above formula to find the bases of the trapezoid.

Calculating the Bases

Using the formula: Midline (m) = (a + b) / 2 Difference between bases (d) = |a - b|

We can rearrange the formula to solve for the bases: a = m + (d / 2) b = m - (d / 2)

Substituting the given values: a = 7 + (4 / 2) = 7 + 2 = 9 cm b = 7 - (4 / 2) = 7 - 2 = 5 cm

Therefore, the bases of the trapezoid are: Base a = 9 cm Base b = 5 cm

This calculation shows that the bases of the trapezoid are 9 cm and 5 cm, respectively.